I like sorting characters from other fandoms - a lot. I’ve been debating doing these in blog posts rather than in various threads, and… well, now I am.
I use the sortinghatchats system - +here’s (M to be safe) a link to their ‘basics’ post. To briefly summarize, though, they sort everyone on two different (and equally important) aspects of their personality: the first (your “primary” house) is why you do things, where the second (your “secondary” house) is how you do things.
And now I’m going to sort the Arrowverse’s Barry Allen.
Primary (the “why”)
Barry is a little tough to sort, because he can look like a lot of different things. The only primary he doesn't look much like is Ravenclaw’s. I’ve second-guessed myself a fair amount as I’ve gone through the series, so I’m going to just look at the other three houses one by one.
Slytherin Primaries prioritize individual loyalties and find their moral core in protecting and caring for the people they are closest to. They often construct a morality system to deal with situations that are not addressed by their loyalty system.
It’s probably the easiest to pick out when Barry has shown a Slytherin side: they’re some of the most significant decisions he’s made, and they’ve had lasting consequences. Changing the timeline to save his parents and his fixation on saving Iris to the exclusion of almost everything else (both in season three) were both motivated by his individual loyalties.
However, the key here is that Barry isn’t truly comfortable with the selfish choices that he’s made. He feels an enormous amount of guilt over them. A Slytherin primary wouldn’t be wrecked with guilt over Flashpoint the way Barry is, for example. It’s also important that, even at his lowest and most unhappy, Barry doesn’t look anything like a petrified Slytherin primary. He never stops caring about the people in his inner circle, and even when he cuts himself off from them at the beginning of season two, it’s not because having people close to him is dangerous to him - he’s (somewhat justifiably) afraid that it’s dangerous for them.
I think Barry fits better with one of the ‘felt’ houses - i.e., Gryffindor or Hufflepuff, which can look quite a bit alike. They trust their guts; they don’t need to pick feelings apart to know that they’re real.
But Gryffindors are also idealists, where Hufflepuffs are loyalists. For Gryffindors, the impact their actions have on people helps shape what they think is right and what they think is wrong, but there’s a bigger picture; for Hufflepuffs, people are the big picture. The end result is often the same, but how they get there isn’t.
Let’s look at Hufflepuff first.
Hufflepuff Primaries value people. They value community, bond to groups, and they make their decisions off of who is in the most need and who is the most vulnerable and who they can help. They value fairness because every person is a person and feel best when they give everyone a fair chance.
This looks a lot more like Barry than Slytherin does. He forms strong bonds with his team at STAR Labs very quickly, and his focus is invariably on saving people who are vulnerable. He wants the world to be fair, and he embodies that when he doesn’t just give members of his team second chances - he dismisses their apologies as unnecessary. He does it for Cisco when he reveals Barry’s identity to Leonard Snart to save his brother. He does it when Harry steals Barry’s speed to save his daughter. He does it when Caitlin turns into Killer Frost and helps Savitar.
Hufflepuff could fit Barry - but it’s not the best fit for him.
Gryffindor Primaries trust their moral intuitions. They feel what’s right in their gut, and that matters and guides them. If they don’t listen to and act on that, it feels immoral.
Barry is a forgiving person, but that doesn’t automatically make him a Hufflepuff. A Hufflepuff might forgive or help someone they dislike because people have inherent worth. That’s not Barry - he’ll forgive people because he believes they’re better than their mistakes and have the right approach inside of them, not because they have innate worth. It’s not just about his friends, either - he forgives Leonard Snart because he believes that Snart is better than that. People who he doesn’t see the capacity to change in are locked up in the pipeline.
Barry is also more than willing to sacrifice social harmony when if conflicts with doing what’s right. He'd certainly prefer for the people around him to get along and agree with him, but Barry doesn’t need them to get along or agree with him. That’s a pattern established in the very first episode, and it runs throughout the series: if Barry thinks that something is right, he’ll do it, and screw what anyone else says. “I’m sorry, but you can’t talk me out of this” or “I’ve made up my mind” are used over and over and over again - and for Barry, social harmony is collateral damage that he doesn’t hesitate to accept if it means that he’s doing The Right Thing. A Hufflepuff would care about preserving it; a Gryffindor wouldn’t.
And while Barry’s attachment to his ever-expanding team at STAR Labs is significant, the nature of that attachment points at a Gryffindor primary, too. His core identity doesn’t revolve around STAR Labs - it revolves around being the Flash. He doesn’t seek out a new community to get involved with in Flashpoint until it becomes intrinsically connected to doing the right thing. And, in the original timeline, his passion for his ideals drags the team out of a thick malaise and brings people together to work toward his vision. That’s far more characteristic of a Gryffindor primary than a Hufflepuff primary.
Throughout the first season, Barry has a decision to make over (and over, and over): should he break his father out of jail? He wants to, but he doesn’t. Part of that is knowing that his father wouldn’t want that, but part of it is that Barry feels like it would be <i>wrong.</i>
The other key is to look at Barry not just at his best, but at his worst. Barry at his worst doesn’t really look much like a burned Puff primary - he never really sees having a community as inherently unsafe, nor does he ever try to shrink it, with the possible exception of stepping away from it in the beginning of season two. However, Barry at his worst looks a lot like a Gryffindor primary who’s starting to strip - he’s never at his most anguished than he is when he doesn’t know what’s right.
It’s true that some of his alter-egos do look a bit like burned Puffs - both Savitar and future!Barry in season three have stepped away from their communities in ways that are a little more characteristic of a burned Hufflepuff than a stripped Gryffindor. However, there’s too much about their journeys and internal struggles that we just don’t see to sway me. It’s entirely possible that future!Barry’s experience surrounding Iris’s death involved something that shook his faith in his ability to tell right from wrong, and it wouldn’t be shocking to see a Gryffindor primary in that position wall themselves off. Similarly, if Savitar was truly ostracized from the group, I can absolutely see his feelings about right and wrong becoming warped. We don’t get to know future!Barry or Savitar well enough to puzzle that out, and their characterization isn’t inconsistent with Gryffindor, so I’m going to stick with my original conclusion: Barry Allen is a Gryffindor primary.
Secondary (the “how”)
His secondary is a lot more straightforward. His team at STAR Labs improvises and plans, and he works hard to improve his speed, but none of that is who Barry is. Charging is who Barry is. Inspiring is who Barry is. And that's all Gryffindor secondary.
Gryffindor Secondaries charge. They meet the world head-on and challenge it to do its worst. Gryffindor Secondaries are honest, brash, and bold in pursuit of things they care about. Known for their bravery, it is almost a moral matter to stay true to themselves in any situation that they’re in.
“Brash” is perhaps a bit harsh, but as “Wells” once pointed out, he’s a bit of a show-off. His pure glee at being mugged in S1 E7 and at helping Joe and Eddie fight criminals after Eddie finds out that he’s the Flash speaks to that.
Whether something’s seen as possible doesn’t really enter the equation - Barry’s sentiment is always “I have to try.” Sometimes that involves using his powers - he does what his team thinks is impossible that against both of the Margon brothers - but it doesn’t always involve it. His unsuccessful appeal to Abra Kadabra’s better nature in season three to learn who Savitar is a great example of how he uses it in a verbal capacity as well as a physical one. He even (briefly) manages to break through to Savitar himself.
His attempts don’t always fail, either - they’re often quite successful. He inspires the people around him with his hope, optimism, and sincerity. Eobard Thawne came back in time to kill Barry, but while his initial motivation in creating the Flash was clearly just to get back to his own time, he clearly comes to feel genuine affection toward Barry, leaving him both STAR Labs and a taped confession for Nora Allen’s murder. Barry pulls Caitlin back from the brink of becoming Killer Frost in episode 7 of season three because he trusts her. Future!Barry was broken by Iris’s death; Present!Barry inspires him to reconnect with the team members and become the Flash again when he goes off to fight Mirror Master and Top, because it’s The Right Thing To Do. “I heard what you said, and you were right.”
Barry doesn’t just inspire the people around him to be better, either - he also inspires them to be honest. He tells them how he feels and what he knows: he’s honest about he remembers from the night his mother died, he’s honest about his feelings for Iris, he’s honest about Flashpoint. It causes him clear distress when he hides things from people - Barry’s default state is being an open book. While he can accept that it’s not always possible, he doesn’t like it, because he often isn’t deciding to tell people things so much as being too earnest not to tell them.
It being a “moral matter” to stay true to himself is a perfect description of where his struggle comes from in S1 after he discovers that “Wells” was involved in his mother’s murder. Joe can fake it. Barry can’t. If he tells you that he’s going to do something, he will do it. He tells his father he’ll free him from prison, and he does. He promises to go back for the real Jay (twice!), and he does. He promises to save Iris, and he does (albeit with assistance from HR). Yes, he’s saving people he cares about (or identifies with) - but it’s often clear that Barry’s motivated by the principle as much as the practical implications. He doesn’t break promises because that’s just not what you do.
In summary: Barry is a Gryffindor primary and a Gryffindor secondary.